diff --git a/build-fuzz-corpus-multiple-sizes.sh b/build-fuzz-corpus-multiple-sizes.sh
index 268d306a..3581f55e 100755
--- a/build-fuzz-corpus-multiple-sizes.sh
+++ b/build-fuzz-corpus-multiple-sizes.sh
@@ -1,6 +1,16 @@
 #!/bin/bash
 set -euxo pipefail
 mkdir "fuzz/corpus/fuzz_$1_recombination_sources" || true
+
+# Ensure all 0-byte, 1-byte and 2-byte strings are eligible for recombination
+touch fuzz/corpus/fuzz_write_recombination_sources/empty
+for i in $(seq 0 255); do
+  printf "%02X" "$i" | xargs -n 1 -I '{}' sh -c 'echo {} | xxd -r -p > fuzz/corpus/fuzz_write_recombination_sources/{}'
+  for j in $(seq 0 255); do
+    printf "%02X%02X" "$i" "$j" | xargs -n 1 -I '{}' sh -c 'echo {} | xxd -r -p > fuzz/corpus/fuzz_write_recombination_sources/{}'
+  done
+done
+
 for size in "${@:2}"; do
   echo "$(date): STARTING ON SIZE $size"
   rm -rf "fuzz/corpus/fuzz_$1_pre_fresh_blood" || true